1. Field of the Invention
The invention relates to design of layouts used in lithography of semiconductor wafers. More specifically, the invention relates to a method and an apparatus for applying proximity corrections to layouts of integrated circuit (IC) chips.
2. Related Art
In the manufacture of integrated circuit (IC) chips, minimum feature sizes have been shrinking according to Moore's law. Currently the minimum feature size is smaller than the wavelength of light used in the optical imaging system. In order to achieve reasonable fidelity (including resolution and depth of focus) between (a) a layout designed in a computer and (b) shapes of circuit elements formed in a wafer after fabrication, a number of reticle enhancement technologies (RET) have been developed over the last decade, such as optical proximity correction (OPC), phase shifting masks (PSM), and sub-resolution assist features.
Proximity correction as performed in prior art, is briefly described below. First an originally-drawn shape called layout (or pattern) 10 is created in a computer (see FIG. 1A) by use of electronic design automation (EDA) software available from, for example, Synopsys, Inc. Then layout 10 is etched into a standard mask 12. Mask 12 is then used to form a wafer, using a lithography process during which pattern 10 is subject to optical effects 14, resist effects 16, and etch effects 18. The result is an uncorrected wafer structure 20 (FIG. 1A) which contains a number of deviations from layout 10.
One or more such differences between structure 20 and original layout 10 may be measured and used to identify wafer proximity corrections 30 (FIG. 1B). Wafer proximity corrections 30 are then used to overcome this specific set of optical effects 14, resist effects 16, and etch effects 18 when using layout 10 to form a wafer. Specifically, as shown in FIG. 1B, layout 10 is subjected to wafer proximity corrections 30 to form a corrected mask 32. Use of corrected mask 32 in lithography results in a corrected wafer structure 40 with significantly fewer deviations from pattern 10.
Wafer proximity corrections 30 may be obtained, by overlaying on original layout 10, a number of predetermined shapes called “serifs”. These serifs may add or remove area from the layout. FIGS. 1C and 1D illustrate a portion of an original layout 81 (FIG. 1C) and an adjusted version thereof obtained by addition of square shaped serifs 83-89 (FIG. 1D). Although serifs 83-89 are illustrated as square in shape, other shapes such as rectangles or long lines of effectively infinite length and finite width may be used. The size of each of serifs 83-89 is selected depending on a specific amount of deviation at individual x-y locations in structure 20 (FIG. 1A) relative to corresponding locations in original layout 10.
Wafer proximity corrections 30 may be obtained by forming, in a computer, a model of a wafer fabrication process (“process model”) using one or more convolution kernels to simulate the wafer image distribution that results from a lithography process. The term “intensity” is sometimes used to denote wafer image distribution resulting from a combination of optical effects 14, resist effects 16, and etch effects 18 of a semiconductor wafer fabrication process to create a layer in the wafer, for example, a metal layer or a polysilicon layer. Such a distribution is typically generated from a kernel-based model of the fabrication process (including each of optical effects 14, resist effects 16, and etch effects 18), by convolving an IC layout with convolution kernels to obtain a simulated wafer image. Convolution kernels used in prior art, to model a wafer fabrication process, are shown in FIGS. 1F-1O.
The specific convolution kernels that are used in a process model are normally identified by a supplier of the model. The supplier may generate the process model by empirically fitting data from test wafers using any conventional software such as Progen™, a lithography model development tool available from Synopsys, Inc. or Calibre™ available from Mentor Graphics, Inc.
A process model typically contains a set of spatial filtering kernels (FIGS. 1F-1O), where the 2 dimensional kernel surface is defined as an algebraic expression, or as numerical values on a grid of 2-D points. Each of these kernels will be convolved against an IC mask layer. The mask layer is a 2-dimensional surface defined by polygons where the value of the surface inside the polygon is 1, and 0 outside the polygon (or vice versa for a clear field mask). The process model also contains one or more algebraic expression(s) describing how to combine the convolution results into an intensity surface. The process model also contains an algebraic expression (typically a constant) describing a threshold value for drawing contours in the process intensity surface.
For more information on making and using process models, see the following articles all of which are incorporated by reference herein in their entirety as background:    Title: Optimizing proximity correction for wafer fabrication processes.    Author: Stirniman, John P.; Rieger, Michael L.    Conference: 14th Annual Bacus Symposium on Photomask Technology and Management Santa Clara, Calif., Sep. 14-16, 1994.    Publication: Proc. SPIE—Int. Soc. Opt. Eng. (USA), vol 2322, p. 239, 1994    Title: Quantifying proximity and related effects in advanced wafer processes.    Author: Stirniman, John P.; Rieger, Michael L; Gleason, Robert.    Conference: Optical/Laser Microlithography VIII; San Jose Calif.; Feb. 20-22, 1995    Publication: Proc. SPIE—Int. Soc. Opt. Eng. (USA), vol. 2322, p. 252, 1995    Title: Characterization and correction of optical proximity effects in deep-ultraviolet lithography using behavior modeling.    Author: Yen, A; Tritchkov, A; Stirniman, J; Vandenberghe, G; Jonckheere, R; Ronse, K; Van den hove, L;    Conference: American Vacuum Society; Microelectronics and Nanometer Structures    Publication: J. Vac. Sci. Technol. B 14(6), p. 4175 November/December 1996    Title: Spatial filter models to describe IC lithographic behavior    Author: Stirniman, John P.; Rieger, Michael L.    Conference: Optical Microlithography X; San Jose Calif.; Mar. 12-14, 1997    Publication: Proc. SPIE—Int. Soc. Opt. Eng. (USA), vol 3051, p. 469, 1997    Title: Optical proximity effects correction at 0.25 um incorporating process variations in lithography.    Author: Tritchkov, A.; Rieger, M.; Stirniman, J.; Yen, A.; Ronse, K.; Vandenberghe, G.; Van den hove, L.    Conference: Optical/Laser Microlithography X; San Jose Calif.; Mar. 12-14, 1997    Publication: Proc. SPIE—Int. Soc. Opt. Eng. (USA), vol 3051, p. 726, 1997    Title: 0.18 um KrF lithography using OPC based on empirical behavior modeling.    Author: Tritchkov, A; Stirniman, J; Gangala, H; Ronse, K    Conference: American Vacuum Society; Microelectronics and Nanometer Structures    Publication: J. Vac. Sci. Technol. B 14(6), p. 3398 November/December 1998    Title: Automated OPC application in advanced lithography    Author: Kurt Ronse, Alexander Tritchkov, John Randall,    Conference: Bacus PhotoMask Japan Symposium, Kanagawa, April 1997    Title: Universal Process Modeling with FTRE for OPC,    Author: Yuri Granik, Nick Cobb, Thuy Do,    Conference: Optical Lithography XV, Proceedings SPIE Vol. 4691, 2002.    Title: New Process Models for OPC at sub-90 nm Nodes,    Author: Yuri Granik, Nick Cobb,    Conference: Optical Lithography XVI, Proceedings SPIE Vol, 5040, 2003    Title: Model-based OPC considering process window aspects: a study,    Author: S. F. Schulze, O. Park, R. Zimmermann, et al.,    Conference: Optical Lithography XV, Vol 4691, 2002
Explicit descriptions of the process model expressions that are conventionally used to combine convolution values at a given location in a layout, to generate an intensity value at that location, are provided in a number of prior art publications, such as the following articles all of which are incorporated by reference herein in their entirety as background:                Y Pati, T Kailath, Phase shifting masks for microlithography, automated design and mask requirements, Journal of the Optical Society of America, Optics Image Science and Vision, 11 No9:2438-2452, 1994;        N. Cobb, A. Zakhor, Fast Sparse Aerial Image Calculation for OPC, Bacus 1994, SPIE Vol 2621, p534-545, 1995;        Mathematical and CAD framework for Proximity Correction, Nick Cobb, Avideh Zakhor, Eugene Miloslavsky, SPIE, Vol 2726, p208-222, section 3, 1996);        H Liao, S Palmer, K Sadra, “Variable Threshold Optical Proximity Correction (OPC) Models for High Performance 0.18 um Process, SPIE, Vol 4000, p 1033-1040, 2000; and        J Randall, K Ronse, T Marschner, M Goethals, M Ercken, “Variable Threshold Resist Models of Lithography Simulation, SPIE 3679, p 176-182, 1999.        
Prior art methods of proximity correction involve a first application of a process model to an unperturbed layout, to obtain an unperturbed intensity surface (or value at a point) which represents the wafer's image distribution as a function of location (x, y) (or at a single point). Thereafter, the layout is perturbed by adding or removing a serif of an initial serif size, followed by a re-application (i.e. a second application) of the process model to the perturbed layout to obtain a perturbed intensity surface or a perturbed intensity value at a point. The initial serif size, when scaled by a ratio of (a) a difference between a threshold and unperturbed intensity and (b) a difference between the perturbed intensity and the unperturbed intensity, yields a serif size used in proximity correction. In current commercial tools known to this inventor, the second application of the process model is performed iteratively, until the individual serif is properly sized to within a predefined tolerance.
The just-described second application of the process model is typically performed 1000s of times, once for each location (x, y) where one wishes to place a serif In the end, when the original layout has been adjusted at sufficient locations, a simulated wafer image (from using all the proximity corrections) conforms to the original (unadjusted) layout sufficiently to proceed to actual fabrication of production wafers.
Note that a second application of the process model is required for every serif, because current prior art known to this inventor does not teach how to separately account for the individual intensity contribution from an individual serif. Such an individual contribution cannot be simply added to an earlier computed intensity when the process model is non-linear. In practice, process models are at least 2nd order non-linear, as both optical energy and optical coherence effects are second order. The prior art known to this inventor always re-evaluates the process model after every perturbation in the layout shape. This inventor notes that the two applications of the process model, once without the serif, and a second evaluation with the serif, are providing a numerical response of the process model intensity with respect to the serif, without modeling sensitivity as described herein by this inventor, after this background section.
After proximity corrections are identified as described above, a corrected mask is created using a proximity corrected layout (see step 48 in FIG. 1E), followed by use of the corrected mask, in lithography and related wafer fabrication processes (see step 42″), to produce a production wafer 40′ having the corrected layout (i.e. this layout sufficiently conforms to the originally-designed unadjusted layout). As shown in FIG. 1E, a test wafer 20′ may be initially used to formulate a correction recipe 44 that is stored in a recipe library 46 for use in proximity correction 30 of new IC designs 10″.
In the process described in paragraph [0008], the most compute intensive work is performed in applying a process model to a layout, which as noted above requires a second application of the process model for each serif U.S. Pat. Nos. 6,081,658 and 6,289,499 that are incorporated by reference herein in their entirety, describe fast convolution methods for calculating intensity at a single location. These methods can be used to apply a process model to a layout as often as needed, and they operate in the space domain. All commercial full-chip proximity correction tools known to this inventor use this space domain, fast convolution method for process model evaluation. To calculate the effect of a perturbation, these tools rely on two calls to the process model—one without the serif and a second with the serif. When using the fast convolution method, the second application of the process model is fast enough to make full-chip proximity correction tools practical
Application of a process model to a layout for proximity correction can also be performed in the frequency domain using any conventional FFT (fast Fourier transform), to transform the layout into the frequency domain where the convolutions are calculated. See, for example, U.S. Pat. No. 6,263,299 granted to Aleshin, et al. and U.S. Pat. No. 6,171,731 granted to Medvedeva, et al. both of which are incorporated by reference herein in their entirety, as background. Note that these two patents also require the second application of the process model, within the loop over each location where a serif is to be added, as described above in paragraph [0015].
When using the method of FFT to calculate convolutions in a process model, the second application of the process model at each serif is prohibitively expensive. There is currently no known method, to the knowledge of this inventor, to calculate the effect of a perturbation on the process model, without calculating the effect of the perturbation on each of the individual FFT's used in the process model. Because there may be between 4 to 40 separate FFT's used in the application of the process model, calculating the effect of the perturbation on each is cumbersome. Also, to the knowledge of this inventor, an FFT approach is currently not used in any commercially available software for full chip, optical proximity correction, in part because of the inability to calculate the effect of a perturbation quickly.
An article by Yuri Granik published March 2005 in the Proceedings of SPIE Vol. #5754-47, entitled “Solving Inverse Problems of Optical Microlithography” describes a method to calculate the effect of a perturbation in the layout, when using an FFT-based method for the calculation of intensity. Towards the end of this article, in section 5 thereof, Granik suggests that saving electrical fields Ai0 for a mask m0 and calculating the intensity for a slightly different mask m′ as per equation (61) based on the saved fields Ai0, is faster than a second convolution of the perturbed layout by FFT. The convolutions in equation (61) are quickly calculated by direct multiplication, according to Granik. Therefore, Granik calculates the effect of each perturbation on each saved electric field, then applies the process model a second time to calculate a perturbed intensity. Granik's perturbed intensity, the original intensity, and a target intensity are used to calculate a serif size, using the same serif size calculation currently used in commercial tools as described in paragraph [0011].
In Granik's method, computational complexity may be reduced to order (d*M*N), where d is the number of pixels modified in the pattern, M is the number of pixels in the kernel and is typically on order of two-hundred-fifty to twenty thousand, and N is the number of intermediate electric fields and is typically on order of four to forty. Granik states the particular importance of the case where one perturbs a pattern one pixel at a time, where d=1. However, even when d=1, the number of calculations necessary per perturbation is on order of one thousand to one million. Hence, Granik's method appears to be too slow for practical applications.
Furthermore, caching intermediate FFT results requires memory. If an IC design has been divided up into a number of subdivisions of area 100 by 100 micron2, with pixel resolution of 50 nanometers, then each subdivision requires roughly 32M Bytes per FFT. And this value easily grows by another order of magnitude, by increasing the area of the FFT or the decreasing the pixel size. Assuming between 4-40 FFT's in a typical application, this results in 100M to 1.2 G Bytes of cached information in Granik's method, a size far too large to be accessed quickly using cache technologies available in today's computers.
In the above-discussed article, Granik applies the process model a second time for each serif. Although he has proposed a faster method to evaluate the effect of the serif, his calculation still relies on a numerically calculated response, which can be easily identified by his two applications of the process model, with and without a serif. Since the process model in practical applications is non-linear, the second call to the process model at each serif is computationally expensive. In this regard, Granik's method is consistent with current commercial tools which apply the process model a second time at each serif. Granik fails to disclose or suggest a second model of sensitivity, as described herein by this inventor, in text following this background section.
Granik's method also requires saving the intermediate electric fields. This is another indication that he is calculating a numerical response, as the second application of the process model requires these intermediate electric fields. In the method discussed next, it is not necessary to save (or regenerate) the intermediate electric fields, and hence, not possible to calculate the process model a second time.
It is well known in the prior art to compute a parameter called “mask error factor” (MEF) as the change in an imaged edge position per unit change in the corresponding drawn edge position. In the language of OPC, this inventor postulates a MEF equivalent to be the “change in process model contour position per unit change in perturbation width”. Prior art known to the inventor calculates MEF numerically, by calling the process model twice as noted above: once without the perturbation, once with the perturbation. Thereafter, the two corresponding contours are calculated, followed by taking the difference, and calculate the MEF as the change in the contour difference divided by the size of the perturbation. To the knowledge of this inventor, there is no prior art method to derive an algebraic MEF sensitivity function which defines the MEF at any arbitrary polygon edge.